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Spread of epidemic disease on networks
Phys. Rev. E 66, 016128 – Published 26 July, 2002
DOI: https://doi.org/10.1103/PhysRevE.66.016128
Abstract
The study of social networks, and in particular the spread of disease on networks, has attracted considerable recent attention in the physics community. In this paper, we show that a large class of standard epidemiological models, the so-called susceptible/infective/removed (SIR) models can be solved exactly on a wide variety of networks. In addition to the standard but unrealistic case of fixed infectiveness time and fixed and uncorrelated probability of transmission between all pairs of individuals, we solve cases in which times and probabilities are nonuniform and correlated. We also consider one simple case of an epidemic in a structured population, that of a sexually transmitted disease in a population divided into men and women. We confirm the correctness of our exact solutions with numerical simulations of SIR epidemics on networks.
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Physical Review E 25th Anniversary Milestones
The year 2018 marks the 25th anniversary of Physical Review E. To celebrate the journal’s rich legacy, during the upcoming year we highlight a series of papers that made important contributions to their field. These milestone articles were nominated by members of the Editorial Board of Physical Review E, in collaboration with the journal’s editors. The 25 milestone articles, including an article for each calendar year from 1993 through 2017 and spanning all major subject areas of the journal, will be unveiled in chronological order and will be featured on the journal website.
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- One should observe that the network studied in Ref. [8] is a cumulative network of actual sexual contacts—it represents the sum of all contacts over a specified period of time. Although this is similar to other networks of sexual contacts studied previously [50][51] it is not the network required by our models, which is the instantaneous network of connections (not contacts—see Sec. II). While the network measured may be a reasonable proxy for the network we need, it is not known if this is the case.
- It is also worth noting that networks of sexual contacts observed in sociometric studies [51] are often highly dendritic, with few short loops, indicating that the treelike components of our percolating clusters may be, at least in this respect, quite a good approximation to the shape of real STD outbreaks.